Modern Simple Mathematics Part 3

Modern
Simple
Mathematics

By
Council for Preparation Of Textbooks

Translated By
Irfan Ahmed Siddiqui

Pea eee

The books are frequently revised and updated to meet the challenges
of the fast changing world in the fields of science and technology , new
developments in the methodology of teaching and growing needs of the
students to understand the subject through simple, lucid and illustrative
method.

The book in your hands i.e. Modern Simple Mathematics is the part
of our plan to revise all our textbooks.

The thoughts and views which have a direct influence on the lives of
the students and are associated with the real purpose of their lives have been E
given due importance and consideration in the preparation of this book.

Keeping in mind the general and prevailing perception among the |
students, the parents and of course the teachers that Mathematics is a dull
and boring subject, we have designed this book so as to allay such Maths |
phobia among these people. Moreover, efforts have been made to clear each |
and every point by profusely illustrating the book with sufficient solved
examples, graphics and instructions for teachers wherever necessary The
exercises have been designed to relate them with the day-to-day needs of
the students.

We acknowledge all those whose kind cooperation, guidance and
assistance have culminated inthe production of this book.

Suggestions and comments are highly appreciated a Le be
thankfully acknowledged.

New Delhi Mohd. Ashfaque Ahm
20.08.2013 : (Incharge)

The need and utility of Mathematics in our day-to-day life is
universally acknowledged. No one can eventually do without the
basic concept of Mathematics - whatsoever profession one is
in.Everyone has to deal, more or less, with personal and family
budget,marketing, mutual give-and-take, measurement, Zakat and
Ushr inheritance and other obligations. That is why the practice of
teaching basic Mathematics to little children from the very beginning
has been in vogue for centuries. And in this age of science and
technology this need has assumed much more importance.
Inventions, industries and scientific developments in the various
fields have left an abiding influence on the very course of our life.
Whether it is industry or handloom, business or agriculture, science
or technology, the knowledge of Mathematics is required at every
step. Thus for the success of life it is essential that every pupil is
taught Mathematics up to the secondary level.

Not only to meet practical needs of life, the knowledge of basic
concepts of Mathematics is necessary to gain mastery over different
subjects, to study science and social sciences and even the books of
language and to understand them quite well.

Children do require the knowledge of counting, addition,
subtraction and other details of weighing and measurement in doing
work at home and school, in knowing the quantity and number ,
shape and size of things, in business transactions, in games anc
sports and in satisfying their curiosity at every step in their da
day life. For the fulfilment of this need it is necessary to teach the
Mathematics. This is the most important subject next only
basic knowledge of Islam and the mother tongue. Thus it sh
given special attention accordingly. .

Modern Simple Mathematics

The real purpose of teaching Mathematics at th
gradually develop so much awareness in childr
mathematical problems in their day-to-day life, as
number as well as shape and size of the things they
business transactions, have suficient knowledge
measurement as well as time and distance, and make
Mathematics. To achieve this purpose it is in
Mathematics at the elementary level.

(Late) Afzal Hussain, M.A.; L.T

odern Simple Mathematics - 3

oP TERS Page No.

Revision

Reading and Writing of five-digit numbers
Addition 3

Subtraction 19
Tables 21
Multiplication 24
Division 30
Indian Currency 32
Measures of Mass 36
Measures of Length 41
Measures of Time 48
Fractional Numbers 52

Geometrical Shapes

Modern Simple Mathematics - 3

CHAPTER - 1

Revision
EXERCISE-1.1
Tables: Oral

Fill in the blanks with the help of tables:

Modern Simple Mathematics - 3

EXERCISE-1.2

1. Write the Bap ssctipig numbers i in words:

2. Write the place value of all the digits in the number “4759”.

3. Using the blocks on the right side, answer the following questions:

(a) Write in figures the numbers written in the blocks.

(b) Find the sum of the first four blocks. (1)

(c) Find the product of the numbers (2)
in the first and second blocks. (3)

(d) Subtract the number in the fifth (4)
block from the number in the
fourth block.

(5)

In two-three digit numbers, the number with greater

digit at Hundreds place is greater

=> If the Hundreds digits in the given numbers are the
same, the number with greater digit at Tens place is
greater.

=> If Hundreds and Tens digits are both the same, the
number with greater digit at Ones place is greater

>moSthenr

Modern Simple Mathematics - 3

Write the numbers in ascending and descending order, formed
by the following digits:

(A) 8, 6, 4 (Bs, 95
5. Write the greatest and the smallest 3-digit numbers.

EXERCISE-1.3

Number Game: Add the numbers of following puzzle as directed
ES

2 2+9+4=15
4+5+6=15
EF: 253-8 =15
6+1+8=15
+6 94+541=15

1. From left to right
Sum of firstrow = 2+9+4 = 15
Sum of second row = 0 ~w3rerera-
Sum of third row = 2 rwrererese-
2. From top to bottom (Downward)
Sum of firstrow = 24749 =15
Sum of second row = = -wrnrnen=-oo--
Sum of thirdrow = 0 rwrrrenee-
3. From upper left corner to lower right corner (Diagonally)
Sum of three digits = = 2+5+8 = 15

4. From upper right corner to lower left corner (Diagonally)
Sum of three digits = 0 -wserreanee

From above puzzle, we observe that the sum of digits of each row,
column and diagonal is same as 15.

Modern Simple Mathematics - 3

5. Complete the following puzzles with suitable digits so that the sum of

each row, column and diagonal should be same:

If Asghar deposits 5 rupees daily, how much will he deposit in a week?
How much is it short of fifty rupees?

; 2. After exams, the school was closed for 3 days from Monday. On which
H day will the school reopen?

3. Rahmat went home from Hostel on Sunday evening and returned on
H Thursday evening. For how many days was he on leave?

4. Students of a school went on picnic on Sunday and returned the third
i day. Which day was it?

5. Apencil costs 75 paise. How much will 3 pencils cost?

i 6. Nine passengers of a bus purchased an orange for 95p each. How much
H money did the orange seller get?

7. Sajid bought one kilogram of ghee at the rate of 350 rupees a kilo

: and gave a five hundred rupee note to the shopkeeper. How much

i money did the shopkeeper return to sajid?

i 8. Measure with a scale the length and breadth of your Mathematics book?
i 9. Ifashirt needs 2 metre cloth, how many shirts can be prepared with 12
i metre cloth?

10. A matchstick is 4 cm long. How long will 50 sticks be if kept end to end?
: 11. Half Kg flour is consumed in a house daily. How much flour will be
: comsumed in 8 days?

Modern Simple Mathematics -

CHAPTER - 2

Reading and writing of 5-digit numbers

You have learnt reading and writing of 3 and 4-digit numbers. You .
can also tell the smallest and the largest 3 and 4-digit numbers.

You know that the largest 3-digit number is 999 and largest 4-digit
number is 9999. You also know that if one is added to them we
get1000 and 10000 respectively. You can write 7000, 8000 and 9000.

If 3 zeroes are written to the right of 10, we get 10 000 or Ten thousand,
similarly if 3 zeroes are written to the right of 11, 12, 13,..... we get
11000, 12000, 13000, ...... (and so on).

11000 Eleven thousand
12 000 Twelve thousand
13 000 Thirteen thousand

Remember: To write ten thousand we put four zeroes next to
1 (right of 1) 10000. This is the smallest 5-digit
number.

Modern Simple Mathematics - 3

EXERCISE-2.1

1. Fill in the blanks adding 1000 in each step upward.
Also say loudly what you write.

2. Fill in the blanks adding 10000 in each step upward.

3. Fourteen thousand students appeared in an examination.
Write this figure in words.

4. There are thirty thousand words in an English book and
eighteen thousand words in G.K. Book. Write these numbers
in figures.

Example : Write Thousands, Hundreds, Tens and Ones
of the number 48,724.

Solution: We can write

48, ale = 40, 000+ 8,000 + 700 + 20+ 4

So, there are 4- Ten thousands, 8- Thousands, 7-Hundreds,
2-Tens and 4- Ones.

Modern Simple Mathematics -

ac“ i a

Note: From Thousands place onwar ds each place can hve a

two-digit number, hence it is better to say that there are
48-Thousands, 7-Hundreds 2-Tens and 4 Ones

Write the following numbers according to the above solve examples
(a) 80543 (b) 32817 (c) 48064 (d) 29138 (e) 23704
(f) 19276 (g) 71850

6. Write the smallest and the greatest 5-digit numbers in both numerals
and words.

Remember: Ten Ones = One Tens
One Hundreds
One Thousands

Ten Tens
Ten Hundreds

EXERCISE-2.2

Write the following numbers in words:
(a) 19751 (b) 2970 (c) 29175 (d) 99259 (e) 85482
: 2. Write the following numbers in figures:
: (a) One hundred thirteen (b) Eight hundred ninety-eight
(c)Two thousand thirty seven (d) Twenty-four thousand eight hundred
i (e) Seventy-five thousand seven hundred three
3. Astudent wrote fifty thousand thirty as 5030. Whether it is correct or
not? If not, write correctly.
: 4, Write the greatest and smallest number formed by digits 7, 6, 5, 0 and 3.
Make as many numbers as possible by using digits 2, 3 and 5 only
once in each number. Arrange them in ascending and descending
orders. Also find the difference between the greatest and the smallest
numbers so formed.

Modern Simple Mathematics - 3

PLACE VALUE

i Value of a digit is shown by the place of it in a number. A digit written
; at different places has different values. See the following examples:

‘In 43527 the place of 7 is at Ones. Hence its value is sel:

“In 45673 the place of 7 is at Tens. Hence its value is = 70

In 23748 the place of 7 is at Hundreds. Hence its value is = 700

In 47530 the place of 7 is at Thousands. Hence its value is = 7000
In 78356 the place of 7 is at Zen Thousands. Hence its value is =70000
You have noticed that 7 changed its value as per its place.

i So, the value of a digit is by virtue of the place it is written.

EXERCISE-2.3

Example: Place value of each digit is shown as under:

| Lo. 4 Ones or 4
6 Tens or 60
5 Hundreds or 500

9 Thousands or 9000
8 Ten Thousands or 80000

1. Write the place value of each digits in the following numbers
according to the solved example:

(i) 546, (ii) 7823, = (iii) 61452, (iv) 21359
2. Write the place value of the underlined digit:

(i) 21566, (ii) 32720, — (iii) 45068, = (iv) 56072
3. Write the place value of both 2s in the number 20425.

Modern Simple Mathematics -

CHAPTER -3

Safwan did the following sum, thus-

643 : 643
37 and Zeeshan did it like 37
589 589

2 2

1271
If you observe these two sums, you find that Zeeshan did it correctly
and hence his answer 1271 is correct. What mistake did Safwan do? He
did not care while writing numbers in column. He must have written digits
having the same place value in the same column.
We will never get correct answer if we don’t care about the place
value of the given numbers.

: Hundreds under Hundreds, Thousands under Thousands and so on.
(3 © Digit of each place is added individuallyAnd if we get a 2-digit number,
___ we write only one digit and carry another to the next place.

: _ © In addition, either add upward or downward, the result will be the

|= Method of adding large numbers is the same as that of small numbers.

Modern Simple Mathematics - 3

Now see the following examples:

Example (1) : 1976 + 5784 + 1632

Solution: Th H T O

@<=, Ox Ox
9 eee! \

1 \ 6

age bee

tel 6 3 2

Result is: 9 3 9 2

Explanation:
Step-1: First we add Ones 6+4+2= 12 i.e. 2 ones and | tens.

2 is written at Ones place and | (Tens) is carried to Tens place. (This
is carry)

Step- 2: Now add Tens 7 + 8 +3 + 1 (carry) = 19. We write 9 in Tens
place and carry 1 (Hundreds) to Hundreds place.

Step-3: Add Hundreds 9+7+6+ 1 (carry) = 23

23 Hundred or 20 Hundreds and 3 Hundreds

20 Hundred or 2-Ten Hundreds or 2 Thousands carried to thousands
place and 3 Hundreds written under Hundreds place.

Step-4: Now finally we add Thousands 1 + 5 + 2 (carry) = 9. We write
it at Thousands place.

Now addition is complete and the sum is 9392.

Example (2): 3786 + 2947 + 6733

Modern Simple Mathematics -

as ae ee cee
(1) Sum of Ones 6 +7 +3 = 16. We write 6 at ones place and
carry | to tens place.
(ii) Sum of Tens including carried 1 = 1+8+4+3= 16.
6 is written at Tens place and 10 Tens or | Hundred carried
to Hundreds place.
(iii) Sum of Hundreds including carried!
=1+7+9+7=24 (Twenty four hundreds)
or 20 Hundred = (Two thousand) and 4 Hundreds. 4 is
written under Hundreds and 2 carried to Thousands place.
(iv) Sum of Thousands (including carried 2)
=2+3+2+6=13
3 is written at thousands place and Ten thousands or 1 Ten
thousand written at Ten thousand place.
So, the answer is 13466.
You can add without actually writing carried numbers
in the column. Thus -

+ 30078
$333.35 + 54653

+44444

4. VRA5 5. 34D8 so, Ura
se a 5". 5 HS) + 23506 of 205°957
des 0 + 14571 + 432

Write the following in column and add:

7. 7798 + 91344
8. 21+ 9562

9. 7+172+ 4651

10. 990 + 9008 + 67097

11. 68067 boys and 27987 girls visited the zoo in August. Find the total
number of children who visited the zoo?

12. A cloth mill manufactured 49549m cloth in January and 73911m in
February . Find the total length of cloth produced in the two months.

13. An electric bulb manufacturing company produced 57308 bulbs in a
year. Another company produced 1350 bulbs and yet another company
produced 17822 bulbs. Find the total number of bulbs produced by
them together.

14. On Eid-ul-Fitr 32715 local people and 28527 outsiders performed Eid
Prayers in an Eid Gah. Find the total number of people offering Eid
Prayers.

15. Aman spent Rs. 19557 on charity and left Rs. 10825 for his family.
How much money did he have?

16. In Rahmat Nagar 21524 persons live in brick-built houses, 22802 in
mud-built houses and 19662 in huts. Find the total number of persons
living in Rahmat Nagar.

Modern Simple Mathematics - 3

CHAPTER - 4
Subtraction

You have already learnt subtraction of 4-digit numbers (up to 9999).
The same method is followed even in the subtraction of higher numbers.
Example (1): Subtract 27432 from 53286

Solution: TTh Th H cE O

: borrow! borrow!
| (10) | Pe 5
3 2 8 6
2 L 4 6) 2
Difference = 2 iS 8 5 4

Subtract Ones from Ones, Tens from Tens, Hundreds from Hundreds and
so on, borrow wherever necessary, write the result under respective
columns.

Example (2): Subtract 14225 from 20056.

Solution: T th , Th H T O

SEI OT
1 B® “810 5 6
1 4 2 2 5
0 5 8 ue 1
Explanation:

Step |. Subtract Ones (5) from Ones (6) =» 6-5 =1

Step II. Subtract Tens (2) from Tens (5) "= 5-2=3

Step III. Subtract Hundreds (2) from Hundreds (0) It not possible.

So borrow from the left number. Since it too has nothing, it will borrow
from its left icc. From Ten Thousand and now Thousands has Ten
Thousands. Now Hundred can borrow one (Thousand) from Thousands to
become Ten Hundreds. At Thousands place there will be 9. Subtract 10

Hundred -2 Hundred =>10-2 = 8

Step IV . Subtract Thousands (4) from Thousands (9)** 9-4=5
Step V. Subtract Ten Thousands (1) from Ten Thousand (1) =» 1-1= 0
Your resultis 5831

Modern Simple Mathematics - 3

Checking: To check your answer do opposite of subtraction i.e. Addition.
Add your result 5831 to the subtracted number 14225.
If you get the number from which you subtracted, your answer is correct.

14225
+5831
20056

EXERCISE-4.1

Find the difference:

1.

95734 2. 44225 3. 60872 4. 67400
—78623 —35216 =55555 —-35644 —

From questions 5 to 8 write the numbers in columns and subtract:
5. 9562-319 6.4657-—275 7. 57265-2523 8. 36782-17861

9°

10.

11.

12.

13.

14.

A school library has 37875 books. How many more books should
be purchased to complete the number of books 40,000.

Subtract forty-eight thousand nine hundred ninety-nine from fifty
thousand.

Arshad bought a radio for Rs.1328 and gave 14 one hundred rupee notes
to the shopkeeper. How much money did the shopkeeper return to him?
Fareed has Rs. 25000. He bought a scooter for Rs. 23625. How

much money is left now?

A contractor manufactured 90602 bricks, out of which 66922 were
sold. How many bricks are left now?

Ambala is enroute Delhi to Simla. If the distance between Delhi and
Simla is 463 Kms and between Delhi and Ambala it is 198 Kms find
the distance between Ambala and Simla.

Delhi

CHAPTER-5 }
Table of Multiplication

If in Darsgah-e-Islami morning prayer there are 4 rows of 10 students bela
how many students are there in all? _

f Solution:
: | Method: By addition

First Row 10 Students
Second Row 10 Students
Third Row 10 Students
Fourth Row +10 Students
Total (sum) = — 40 Students (on adding)

I Method: By Multiplication

Number of students in each row = 10

No. of rows = 4

Total no of students = 40

III Method: Using Table of 10.

t You can easily give correct answer by reading Table of 10 up to 4 i.e. 10 ‘Gare are 40.

i This i is the advantage of Table that save both time and space. You, therefore, should §

learn by heart Table up to 20. There are two methods of making Tables. Simply go oni

i multiplying the numbers by 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 and write the — ies
t time. You’ve got the Table of the desired number .

EXERCISE-5

We get 2 fifty paise coins for | rupee. Find how many 50p coins
will we get for —

(a) 10 rupees (b) 12 rupees (c) 13 rupees (d) 14 rupees
A tin can have 4 Kg of Ghee. How much Ghee will be there in —
(a) 13 tins (b) 14 tins (c) 15 tins

Length of a saree is 5m. Find the total length of —

(a) 11 Sarees (b) 15 Sarees

Modern Simple Mathematics - 3

Solve with the help of Table.

Gi) 11x6= @)= 15 x 6= (iii) 12 x 7=
(iv) 13 x 7= (v) 14x 7= (vi) 11 x 7=
(vii) 15 x 7= (viii) 12 x 7= (ix) 13 x 8=

(x) 14x 8= (xi) Il x 8= (xii)-15* 8: —

Hamid bought 10 stamps of 15 paise each from a Post Office.
How many paise did he spend in all?

A piece of chalk costs 15p each. Find the cost of 6 pieces of chalk.
If a box has 12 pens, how many pens will there be in 6 such boxes?

You used 14 pages daily in solving mathematics problems. How many
pages did you use in a week?

A cycle rider goes 13 kms in an hour. How long will he go in
5 hours?

A boy runs 9 m per second in a race competetion. How long will he
run in 14 seconds?

How many Tens are there in 900?

I have 15 notes of 10 rupee each. How much money do I have?

Sajid reads 5 pages of the Holy Qur’an daily. How many pages will
he read in 14 days?

Mahmood performs 12 Raka’ats of Zuhr prayer daily. How many
Raka’ats will he perform in a week?

Modern Simple Mathematics - 3

- CHAPTER -6

Multiplication

You already know the method of multiplication. “X” is the symbol of

multiplication.
The numbers which are multiplied are called MULTIPLICANDS and the
| result is called PRODUCT

14
‘ ;|—> MULTIPLICANDS
‘S45 => PRODUCE

1 4x 6 is also read as FOURTEEN INTO SIX
(INTO is indication of multiplication)

14 x 6 =8 4 is read as FOURTEEN INTO SIX IS EQUAL TO

EIGHTY-FOUR

You have learned about the multiplication of two or more than two-digit numbers
by a single digit. Now we learn multiplication by two - digit numbers.

Multiplying by 10: Look at the examples below:

13 113
10 10
130 1130

(Zero to the right of 3) (Zero to the right of 13) (Zero to the right of 113)

or

3x10 =3xlTen =3 Tens = 30

13x 10 =13x1 Ten =13 Tens =130

113 x10 = 113x1 Ten = 113 Tens =1130

We observe that while multiplying by 10 only zero is put to the right of
the original number which is to be multiplied by 10, thus

Find the product:
85 x 10
490 x10

15 x10

ae
ae 106 x 10

Il

SE
ae

Modern Simple Mathematics - 3

Multiplying by 20, 30, 40, 50, 60, ete.

Example: 1:- Multiply 147 by 60. Example: 2:- Multiply 351 by 30.

Solution: 147x 60 =147x6Tens Solution: 351 x 30 = 351 x 3 Tens
(147 x 6) Tens = (351 x 3) Tens
882 Tens = 1053 Tens
8820 = 10530

If we have to multiply by 20, 30, 40 ......, simply multiply by 2, 3, 4, .....
and put a zero to the extreme right.

EXERCISE-6.1

{i260 = 9. §9ae40

ae 607 x50 ; 3:25-x 9:0
5: 955 x60 : 846 x70

Multiplying by 100 and 1000.

Example 1:
54 x 100= 54 x 1 Hundred = 54 Hundreds

= 5400
Example 2:

17 x 1000 = 17 x 1 Thousand = 17 Thousands
= 17000

Modern Simple Mathematics - 3

Do as shown in the above example:

15 x 100 = 15 x 1 Hundred = 15 Hundreds = 1500
17 x 1000=
18 x 1000 =
47x 100 =
54 x 1000 =
21-x100- =
35 x 1000 =
70 x 100 =
70 x 1000 =

Multiplying by 10, 100, 1000, 10000 is very easy. Copy the
number and put one, TWo,Three or Four zeroes respectively
to extreme right of the numbers.

EXERCISE-6.2
Find the Product:

1. 15 x1000 = [=] — 2.856 x 100 =

3. 761 x100 = 4. 294 x1000=[___|

5. 405 x1000= [|

Modern Simple Mathematics - 3

Example Multiply 346 by 38

+10380
27 6 8 (multiplied by 8 Ones) 13148

+103 8 0 (multiplied by 3 Tens or 30)
13148 add

Explanation:

We first multiply 346 by 8 ones and then by 3 tens (or 30) and add
the two products.

346 x38 =346x8 = 2768
346 x 30= 10380
add = 13148

x38
(ii) _ First multiply by Ones (8) and write the product 3 4 6

(iii) Now multiply by Tens (3) and start writing product from Tens
column, put a zero at Ones column.

Modern Simple Mathematics -3 §

- Now add these two lines (products); you will get the answer,

i

: (iv)

write in column

Step II {
Step Ill {

Multiply by Ones
Multiply by Tens

Answer = (13148 ]

EXERCISE-6.3
Multiply:

FS Rega TE SEE) EES.

ie eo by 93 Ee 575 by 88
4 1704 by 35. 5. 358 by 93

7. There are 20 Almirahs in a library. Each Almirah has 250 books. How

i many books are there in the library?

8. A bag of rice weighs 35 Kgs. How much will 528 such bags weigh?

9. Cashier of a bank counted 128 notes of 50 rupees. How much money

i did he count?

F 10. On Bareilly -Agra road there are 54 trees at every kilometre. If the

: distance between Bareilly and Agra is 213 km, how many trees are

i there on the road?

i 11. 75 sweaters were pepared for distribution among the poor. If 425 gm

: of wool was used in each sweater, how much wool was needed to
prepare all these sweaters?

; 12. 1500 students of a school collected 15 rupees each for poor students

; 4 fund. How much money was collected by them?

4 13. Aslam memorises 25 Ayats (verses) of the Holy Qur’an. in a week.

How many verses will he memorise in 156 weeks?

Modern Simple Mathematics - 3

Multiplication of 3 numbers

! Example: Find the product, 9 x 12 x 16 i
: Solution : First we multiply 9 & 12, then multiply the product (9x12=108) i
Eby 16. : . ;
: Step 1:12x9 =108 } Step I

x x9

H 108 } Step II
: Step 2: 108 x16 = 1728 X16

: 648

1080

If we change the order of numbers. We observe that there is no change in product

: 12
H : = Step I
| Step 1:12x 16 =192 1 } p

192 } Step II
i Step 2: 192 x 9= 1728 x9

1728

: So, we conclude that there is no change in product, if we change the order of

F given numbers in multiplication.

Find the product:
i" 4 ee 56x 23x 49
3. 8 x54x 152 - 18x 12x 230

Modern Simple Mathematics - 3

CHAPTER - 7

f Dividing two-digit number by one-digit number

i You have 15 bananas to distribute among 5 students; Rashid,
: Majid, Khalid, Huzaifa and Hasan. How will you do?

i 15 bananas, Give one banana to each, remaining = 15-5 = 10
: 10 bananas, give one banana to each, remaining 10-5 = 5
: 5 bananas, give one banana to each, remaining 5-5 = 0
: How much did everyone get * 3 bananas

; (Since you distributed it in 3 Times)

Division

15 distributed among 5; we have to distribute 3 Times.

This you can write thus 3

or 415
0 left
15 distributed among 5 gives 3 with zero left
15 divided by 5 gives 3 with zero remainder

3 [QUOTIENT]
‘DIVISOR ——S)15 ~[DIVIDEND]
-15
“0 =[REMAINDER |
If something is distributed (divided) equally among someones, we
always get zero as remainder.

Modern Simple Mathematics - 3

Learn & Remember:

© Adding the same number again and again is also MULTIPLYING.

© Subtracting the same number again and again from a given number
till we get zero or less than divisor is DIVISION.

® Addition, Subtraction and Multiplication start from right side i.e. Ones
but division begins from left side.

Example:- 36 + 3
| Solution: Step1- First write 36 + 3 in the form of 3) 36

Step2- There are 3 Tens and 6 ones in 36
First of all divide 3 tens by 3. We get 1 as Quotient.

Step3- Now copy 6 ones besides 0 and divide by 3.
We get 2 as quotient and remainder Zero.

Finally we get,
Quotient = 12
Remainder = 0
This division may be written as follows:

ae

Quotient
Dividend

so, 36+ 3 =12

Modern Simple Mathematics - 3

EXERCISE-7.1
Divide:

63 plants were planted in 7 rows equally . How many palnts are

there in each row?

I have 96 toffees. If I give 4 toffees to each boy, how many boys will
get toffees?

Dividing 3-digit number by a single digit number

Example: Divide 952 by 8
Step I: Write itas 8)952

Step II: Divide Hundreds number (since it is on the extreme
left) by 8 (Read the Table of 8 so that you don’t
exceed 9. 8 ones are 8, 8 twos are 16; 16 is greater
than 9) hence it will go one time i.e. Subtract 8 from
9 and write 1 below 8 as remainder.

Step II: Copy down 5 beside 1, now you get 15; divide it by
8 as you divided 9 by 8 earlier. It will again go one
time. Subtract 8 from it and write 7 under 8 as remainder.

Step IV: Copy down 2 beside 7. Now you have 72 to be
divided by 8. Do as earlier.
It will go 9 times (8 nines are 72); subtract. You
get zero as remainder
Now all the digits have been brought down and nothing
more is left to be brought down.

DIVISION IS COMPLETE
Answer: Q=119, R=0

Modern Simple Mathematics -3 §

EXERCISE-7.2

Divide and find the Quotient and remainder:

. Ina gathering on Seeratun-Nabi arrangement for seating 975 students
was made. If5 students sit on one bench, how many benches were
required for all the 975 students?

. 256 bags of wheat were distributed equally among 8 shopkeepers.
How many bags did every shopkeeper get?

Division when first digit from left of dividend is smaller than divisor
Example: Divide 425 by 12

i Solution:

| First we divide 4 Hundred by 12. Since 4 is less than
H 12, it goes zero times 12x 0=0. We write 0 under 4
and subtract; we get 4; now 2 is brought down next
to 4, The number becomes 42.

~ 5 Remainder

Now divide 42 by 12. The Table goes 3 times as
i 12 x 3 = 36; write 36 under 42 and subtract we
get 6. Now bring down 5 beside 6. The number
becomes 65. Now divide 65 by 12. It goes 5 times.
: 12x 5 = 60. Write 60 under 65 and subtract. We get
: 5. Now no more number in the dividend is left to be
brought down. Hence division is Complete. The
answer is Quotient = 35 Remainder = 5.

Modern Simple Mathematics - 3

EXERCISE-7.3

: Divide and find the quotient and the remainder:

7. 520 students took part in a rally. They were in groups of 10
students each. Find the number of groups.
8. A book costs Rs. 15. How many books will be purchased for Rs.930?

Example: Divide 816 by 4

Explanation:
Step I :- Divide 8 Hundreds by 4
It goes 2 times.
On subtracting 8 - 80
Step II: Bring down the next digit i.e. 1
Try dividing | by 4. Since 1< 4, it will go
only zero times. Write 0 above Tens in quotient
and 0 below | and subtract 1-0 = 1
| Step III: Bring down the next digit ie. 6 next to 1; we get 16. Divide 16
by 4. It goes 4 times. The remainder is zero. Now division is complete.

Simple Method

: = Remember :- 1. After bringing down a digit, the new
number thus formed is divided by divisor.

If this newly formed number is less than
divisor, one 0 is put in the quotient and next digit is brought down.
Now it is divided as usual.

Remainder is ALWAYS less than the Divisor. To check your answer -
Multiply Quotient by Divisor and add Remainder. If you get the sum
equal to dividend, then your answer is correct.

Modern Simple Mathematics - 3

MISCLLANEOUS EXERCISE-7.4

Divide and find quotient and remainder. Also check your answer:

10. On the eve of Eid-ul-Fitr, 3520 rupees was collected as Fitra. If Rs.110
was given to each person, how many persons got the Fitra?

11. You can buy 5 toffees for one rupee. For how many rupees will you
get 75 toffees?

12. 360 benches were kept in 15 rooms equally. How many benches are
there in each room? :

13. 300 men offered Juma’ prayer in 12 rows in a mosque. If each row
has equal number of rhen how many men were in each row?

14. 360 students were present in the annual function of a school. If on
every bench only 3 students sat, how many benches were needed in
all to seat all the students?

. Apacket can hold 6 laddoos. How many packets will be required for
144 laddoos?

. A shopkeeper charges Rs 13 for a pair of socks. How many pairs of
socks will he give for Rs. 1365?

. Amango seller kept 1260 mangoes in 14 boxes. If each box has equal
number of mangoes, how many mangoes are there in every box?
For an educational tour Rs. 780 was collected from students. If every
student deposited Rs.15, how many students deposited the money?

. Ina dairy farm 8460 litres of milk is obtained from buffaloes. If each
buffalo gives 15 litres milk, how many buffaloes are there in the farm?

} Modern Simple Mathematics - 3

CHAPTER -8&

Dear children, you often get money for purchasing toffees, vegetables,
fruit, etc. You get it in the form of 50 paise, or one-rupee, two-rupee, five-
rupee coins or notes. You recognise them well.

Have you seen coins of 1 paisa, 2 paise, 3 paise, 5 paise, 10
paise, 20 paise, and 25 paise etc. May be many of you haven’t seen them.
Ask your teacher to show you these old coins if he can arrange.

Your father would have not only seen but also used these coins. Now
these coins are not in use.

Coins now in use are — 10 rupees, 5 rupees, 2 rupees, one rupee,
and 50 paise.

Notes in use :- | rupee, 2 rupees, 5 rupees, 10 rupees, 20 rupees,
50 rupees, 100 rupees, 500 rupees and 1000 rupees.

How many coins and notes have you seen/used
Can you recognise all of them on seeing?
You can also count ten rupees in different coins / notes:

2 coins/notesof 5 rupees = Ten rupees

5 coins/notesof 2 rupees = Tenrupees
10 coins / notes of 1 rupee = — Tenrupees
20 coins of 50 paise = _Ten rupees

Amount of money:- An amount of money can be expressed in two forms. The first
form is called “long form” (i.e. in words) and second form is called “short form”
(i.e. in figures).

If the cost of one meter polyster is 75 rupees and 55 paise, then we can write it as
Rs. 75.55.

So, long form ™75 rupees and 55 paise

short form™ Rs.75.55
The . (point or dot) separates rupees and paise. On right side of the point are

paise and on the left side are rupees
(Leftside) Point (Right side)

Rupees Paise

Modern Simple Mathematics - 3

If there are only paise, they are written as follows:

75 Paise = Rs. 0.75
50 Paise . 0. 80 Paise = Rs. 0.80
10 Paise 0: 12 Paise
5 Paise 0) 99 Paise

(Note: In paise place, there must be two digits)

This point is also called DECIMAL, since scale of 10 is used in
separating rupees and paise. :

[You will study more about decimal in next classes.]

Conversion of rupees into paise:

We know that one rupee has 100 paise. So, we convert rupees into
paise by multiplying given rupees by 100.

Example1: Convert Rs. 8 into paise.

Solution: we can write,
Rs. 8 = 8x100 paise = 800 paise

Example2: Convert Rs. 12.45 into paise.

Solution: Rs. 12.45 = Rs. 12 and paise 45.
First we convert rupees 12 into paise.
Rs. 12 = 12x100 paise = 1200 paise
Now add the paise 45 to the above paise. we get
Rs. 12.45 = 1200 paise +45 paise = 1245 paise

Or
Simply,
we can convert rupees into paise by removing decimal point

from the given amount. For example:-
Rs. 12.45 = After removing decimal = 1245 paise.

Modern Simple Mathematics - 3

Conversion of paise into rupees:-
We know that rupee | has 100 paise. Hence, to convert paise into rupees,
divide the given paise by 100.

Example 1: Convert 365 paise into rupees.

Solution: | Divide 365 by 100. the obtained remainder stand for paise.

Sa 3
Hence, 365 paise = Rs. 3.65 100 )365

. -300
65

Or

To convert paise into rupees, simply put a decimal point after two
digits from right.

For example: paise 365 = Rs. 3 . 65

Decimal point after.
two digits from right

Example 2: Convert 2009 paise into rupees.

Solution: Put decimal point after two digits from right-
2009 paise = Rs. 20.09

Modern Simple Mathematics - 3

EXERCISE-8.1

9 rupees 65 paise . ll rupees 2 paise
125 rupees 10 paise . 314 rupees 7 paise
817 rupees 52 paise . 1007 rupees 87 paise
3738 rupees 9 paise . 3011 rupees 64 paise
35 paise 10. 7 paise

g in rupees and paise:
2... RS-33:60 . Rs. 508.05
5. Rs.100.10 6. Rs. 120.20

C. Change the following into paise:

1 BS cp BES 25 ARSs OLD 3. Rs. 14.15
4. Rs. 20.05 So RSL Rs. 15.50

Change the following into rupees:
1. 250 paise ~ 2. 635 paise TAS paise
280 paise 704 paise 6. © 771 paise

} Modern Simple Mathematics - 3

Addition and Subtraction of Rupees and Paise are as
Normal Addition and Subtraction

Addition

Example: For construction of a mosque 472 rupees and 90 paise was
collected on the first Friday, 500 rupees on the second
Friday and 569 rupees and 45 paise on the third Friday
How many rupees was collected in all?

: 000
Solution: First Frida’ Rs. 472.90

Second Friday Rs. 500.00
Third Friday Rss2.25 6:9 54:5

Total Rs. 1542.35 was collected

Explanation: | Numbers are arranged in vertical columns as is done in
normal addition.
Care is taken that decimal point comes below one another.
Addition starts from Ones place and continues till the last digit.
After Addition is complete, decimal point is put at its place.
The place of Decimal is always after two digits from the right side.

Modern Simple Mathematics - 3

EXERCISE-8.2
1. Find the sum:

(A) ‘B) ©
ad = a

2. Anwar bought milk for 7 rupees and 75 paise, sugar for 5 rupees
and 25 paise and tea for 3 rupees. How much did he spend?

3. Rupees 65300 and 75 paise was spent on the construction ofa
bridge and 28750 rupees and 50 paise on road construction.
How much money was spent on both?

Subtraction

Subtraction is very much similar to Addition. Numbers are
arranged in vertical column as in Addition and process of
Subtraction is done later. Decimal point is put at its place.

EXERCISE-8.3
Subtract:-

i. Rs: 18 . 75 De RSG] oe 33° Rse' 31927246

Rs. 1 S25 RS: 43 oo. Rs. 1379 - 13
4. Rs.48725 . 18 5. Rs. 8965 . 03 6.” Rs; 4712507
Rs. 6547 . 39 Rs. 3594 . 67

Modern Simple Mathematics - 3

Mahmood bought a ceiling fan for 575 rupees and 50 paise
and paid 364 rupees and 75 paise in cash. How much has

he to pay now?

Solution:

574. -—(})
Cost of fan SI 50
Paid cash — 364 75
Balance 210 75

Explanation: It is impossible to subtract 75 paise from 50 paise. So borrow
rupee | from Rs. 575. Since rupee | has 100 paise, so we get 150 paise at
the place of 50 paise now. After subtraction 75 paise from 150 paise we obtain
75 paise ( 150 - 75 = 75).

Since we have borrowed | rupee from Rs. 575 so we left with Rs. 574
Now subtract Rs. 364 from Rs. 574 and write the result Rs. 210 at the place

: 7. Nabeela has 18 rupees and 70 paise. She lent 9 rupees and 25 ;
paise to her friend. How much does she have now?

8. Children collected 162 rupees and 25 paise for lunch in a picnic.
Zubair spent only Rs. 159.50 on lunch. How much money is now
left?

9. Amjad purchased a bicycle for Rs. 1288.75 and gave 13 notes of
one hundred rupee to the shopkeeper. How much money did the
shopkeeper return to Amjad?

10. Masood’s brother withdrew Rs. 27619.85 from his account for
repair of his house. If Rs. 32540.50 was in his account, how much
money is now left in the account?

11. Rashid has Rs. 882.35. He purchased an almirah for Rs. 498.94.
How much is left with him now?

12. Salim bought cloth for 1636 rupees and 75 paise and gave 4 notes
of 500 rupee. How much did the shopkeeper return to Salim?

13. What should be added to 125 rupees and 48 paise to make it 264

rupees 25 paise?

Modern Simple Mathematics - 3

CHAPTER -9

Measurement of Weight

You know that vegetables, wheat, rice, flour , etc. are sold by weighing.
To weigh these things we need weights of kilogram, gram, etc.

Go to a grocer’s shop and see weights of 1 Kg, 2 Kg, 5 Kg, 10 Kg,
500g, 200g, 100g, 50g etc.

223OQO

Take a weight of 1 Kilogram and observe it carefully

What do you notice? 1 Kg is written on it. These are 1000 grams.
It means, 1 KILOGRAM = 1000 GRAM
1Kg=1000g

Exercise (Oral)

i tka =[ |g 2, HalfKg =| |g
3. QuarterKg = [ale 4. 1000g = fos Kg
5. 6000g = ae Kg 6 000g = Kg

7. A packet of rice weighs 4 Kg and another packet weighs 5 Kg.
How much is the weight of the two packets?

Example 1: convert 5 kg into g
Solution: we know that, 1 kg = 1000g
« 5kg=5 x 1000 g = 5000g

Modern Simple Mathematics - 3

Example 2: _ Convert 6 Kg 300 g into grams.
Solution: 6 Kg 300g 6 Kg and 300 g
6 Kg 6 x 1000 g
6000 g
So 6Kg 300g 6000 g and 300 g
or 6000 g + 300 g

or = ,6300;¢
Example 3: Convert 3250 g into kg and g.

Solution: We know that, 1000 g = Ikg.
+ 3250 g = 3000 g + 250g = 3 kg 250 g
Example 4: Add the following
(i) Kg g (ii) Kg
15 250 23
+4 340 +45

Solution: Addition starts from grams
(i) Kg g Kg

15 250 23
+4 340 +45
19 590 68

or 19 kg 590 g 68 kg 875 g
Example 5: Subtract
(i) Kg
86
-50

Modern Simple Mathematics - 3

"iinet msn

Solution: Subtraction will be start from grams.
(i) Kg gm (ii) Kg
460
275
185 :
or 36kg 185 ¢ or 25kg 110g
Example 6: Majid bought 32 kg 430g fruits and 19 kg 520g sweets. What
is the total weight of fruits and sweets together?
kg
Solution: Weight of fruits = 32
; Weight of sweets = 19

Total weight = 51

EXERCISE-9.1

A. Convert into g:
(I) 2kg 250g=

(iii) 7kg 75 g=

B. Convert into kg and g:
(i) 3075g =
(iii) 9008 g =

Modern Simple Mathematics - 3

: (Begin addition from gram)

7. Add 80 Kg 125 g and 20 Kg 400 g

There are 10 Kg 500 g potato and 6 Kg 250g cauliflower in a
basket. What is the total weight of the vegetabes in the basket?

Aslam’s father bought 25 Kg 750 g wheat and 18 Kg rice from a
ration shop. What is the weight of grains bought by him?

. Subtract: (Begin from eS)

Modern Simple Mathematics - 3

Subtract 35 Kg from 50 Kg 280 g.

8. Aslam bought two big watermelons from market. One melon is 8
Kg 500 g and the other is 5 Kg 150 g. What is the difference in
weight between the two?

9. Weight of Rashid was 25 Kg 375g. A year later he became 26 Kg
500g. How much did his weight increase?

Example: _ Find the product kg g
225
Sees
Solution: first of all multiply g by 4 and write the product —_kg g
900 at the place of g. After that multiply kg by4 6 225

and write the product 24 at the place of kg. X 4
Hence, the product is 24 kg 900 g. 24 900
or 24kg 900g

Exercise: Find the Product:

In a fair price shop 350 g sugar is given to every adult person. If
there are 5 adults in a family, how much sugar will the family get
from the shop?

7. 3 Kg of pulse is consumed in a hostel daily. How much pulse will

be consumed in 2 weeks?

Modern Simple Mathematics - 3

[ Division | is

Example: Divide 750 g by 15.

Solution: We can solve this problem by the simple method 15)750 g
of division. Divide 750 by 15, we get quotient 50 “75
and remainder zero. 00
Hence, the answer is 50g. 00

x
EXERCISE-9.3
Divide: - | EXERCISE-9.3]

1. 994g by 14.2. 135 g by 15

3. Apassenger has 135 Kg of luggage with him. If 3 Coolies carried
the load equally. How much luggage did each Coolie carry?

4. Ina large family 3 Kg of rice is consumed daily. For how many days
will 90 Kg of rice be sufficient?

<i>

Liquids like milk and oil are sold by measuring their volume with a
measure called litre (Short - / ). Millilitre (Short - m/) is smaller than litre.

(ty See 1000 mi
Half/ = 500ml
One fourth / = 250 ml

You might have seen measures of one litre, 500 m/, 200 ml, 100 ml, 50ml

etc. If you have not seen them, request your teacher to show you these. (*

50ml 100ml 200ml 500ml 1000m/ or 1/

Activity: Take a bucket of water and measure it first by 1 | measure,
then by 500ml, 200ml, 100ml measures.

Modern Simple Mathematics - 3

Deringer crear erento WRIST

EXERCISE-9.4

Answer the following:

1/ ne
21 we
Halfa litre §=§£=———————-n/

One fourth litre = ——— _ ml

A packet of milk measures 500ml. How much will 2 packets
measure?

Add 100/ 250mi and 75/ 240 mi. (write in column as above)

Some good persons distributed 120/ 400 m/ milk among weak
children and 95/ 550 ml milk among poor children. How much
milk did they distribute in all?

Tanveer’s mother prepared Kheer from 3/ 500m/ milk and
icecream from one and a half litre milk. How much milk did
she use?

Mohan purchased 81 oil. Then he purchased 8/ 500 m/ more oil.
How much oil did he purchase in all?

Modern Simple Mathematics - 3

12

7, Subtract 2/ 144 ml from 61325 ml.

8. A shopkeeper had 60 / 750 ml edible oil. He sold 8/ 150 ml from
it. How much oil is now left?
. Apitcher had 50/ 500 m/ water. A ball struck the pitcher and
broke it. Now it has only 5/ 200 ml Water. How much water is
spilled over?

: (D) Multiply:
"ieee
4

x

= Modern Simple Mathematics - 3

15 ml of honey is supplied in a small bottle. How much honey
will there be in 12 such bottles?

8. 200 ml kerosene oil is consumed in a stove daily. How much oil
will be consumed in 5 days?

9. The petrol tank of a car has 35/ 120 ml petrol. How much petrol
will be there in 4 such tanks?
(E) Divide:
6157 by 15 2. 45ml by 3
3. 392 ml by 7 4. 280ml by 5

5. A large pot had 1250 mi of milk. It was packed in 5 equal packets.
How much milk is there is each packet?

6. 3500 / kerosene oil was divided equally in 7 canisters. How much

oil is there in each canister?

CHAPTER - 10
Measurement of Length
You might have seen a tailor taking measurement of your shirt and
trousers using a long tape. This tape is called Inch Tape since it bears
marks of inch. Some tapes also bear marks of centimetre and millimetre.

You have used a 6-inch scale. It has marking from 0 to 15 at regular
spacing. This is a 15cm scale.

P23 eee pea aes

Centimeter

A cclothmerchant uses a metallic rod to measure cloth. It is called Meter
since it is one metre long.
One metre = 100 centimetre

in short, metre = m
1m=100cm :
& centimetre = cm
A playground, house and garden, etc. are also measured by a metre scale.
Observe your scale. This is a 15 cm scale. You can measure small objects

as pen, pencil and copy with this scale. There are 10 small marks between
any two numbers. OEE rT are marks of millimetre (in short - mm)

EXERCISE-10.1

A. (1) How many cm are there in 1 m? =

(2) How many cm are there in 3 m? = Se
(3) How many mare therein50cm? = eas

(4) How many mm are there in 2 cm?

Modern Simple Mathematics -

. Some labours made 27m 35cm road
_on the second day. How long road did the
There are two pieces of green cloth in

~ 29cm and another 24m 20cm. What i is t
pieces? ==
2 Add 64m 67cm to 24m 8m.

jogern Simple Mathomates - 3

Te

1m 95cm cloth is required for the frock of Tayyaba and 1m Sem cloth
is required for her sister. How much more cloth is required for Toyyab’ s
frock?

Shadab had 80m 75cm rope for his cot. He used 37m 34cm of rope in
the cot. How much rope is now left?

Ayesha had 32m 75cm rope. She made a bag with some of the rope.
Now she has only 2m 56cm of rope. How much rope did she use in
making the bag?

Multiply:
ea cm 2. m cm 3m cm
15 12 24 9 13 20
x 8 x 5 x 4
4. m cm a: m cm 622m cm
9 3 8 5 25 3
x 15 x 9 x 7

A 4m 16cm long chain is required for one bag. How long chain will
be required for 5 such bags?

1m 5cm curtain is needed for a window and 3m curtain is needed for
a door. How much curtain is needed for 2 windows and 2 doors?

In taking one round of a playground one has to walk 460m. How
long will Hamid walk to make 8 rounds of the playground?

Modern Simple Mathematics

. Divide:
1.- 816cmby6 2. 64cmby4
3. 765cmby9 4. 95cmby5

5. 696 mof rope was cut into equal pieces of 12 m length. Find the number
of pieces.

6. 7 Tent Camps are made from 5418m canvas. How much canvas is
used in each tent?

7. 5mcloth is used in a veil (Naqab). How many veils will be prepared
with 75m cloth?

Wonderful Number 1089

Ask your friend to write secretly any 3-digit number in his note book
in a manner that the difference in Ones and Hundreds digit is 2 or more
than 2. E.g. 317

Now ask him to exchange digits of Ones and Hundreds and note
down the new number => 713.

Now ask him to find the difference between the two. 713-317=396
Ask him to exchange digits of Ones and Hundreds
once again =» 693

Now ask him to add these last two numbers = 396+693=1089

[You may write 1089 on separate paper and give it to your. friend before
asking him to do all these operation. He will be surprised that you have
already told the answer without knowing the number secretly written
by your friend.]

Secret of the puzzle:The result will always be 1089 irrespective of
what number is taken by your friend, as long as he follows your
conditions.

Modern Simple Mathematics - 3

CHAPTER - 11

- Measurement of Time

Dear Children!

You might have seen a clock. A clock has two hands, one big and one
small. The big hand shows minute and the small hand shows hour
Some clocks have three hands, one of which moves so fast that it is
seen moving. :
[The teacher should bring two clocks, one with ‘seconds’ hand and
another without ‘seconds’ hand and show them to students. Ask the
students to recognise the hands of clocks. ]
Some clocks, mostly electronic, show time by digits. Thus 07:15:45.
First two digits show hours; second two digits show minute and last
two digits show seconds. Hour, Minute and Second are separated by
either a single dot (.) or a colon (:).

© Observe the dial of a clock. It shows 12 numbers written in a circle.
There are 5 divisions between any two numbers. The number shows
hours and small divisions show minute.

© When the big hand is on 12 and the small hand on
4, we say it is 4 O’clock. Similarly when the small
hand points at 6 and the big hand points at 12, we
say it is 6 O’clock.

Minute Hand

Hour Hand
Second Hand

4 O’clock
Example: Look at the folllowing picture of clock. It shows 3 O’clock.

The minute hand is on 12.

The hour hand is on 3.

EXERCISE-11.1

1. Sce the picture of the clocks and write time under each clock.

2. Where will be the hour and the minute hands at —
Hour Hand at Minute Hand at
2 O’clock See Saree es
7 O’clock
12 O’clock

9 O'clock

© See the dial of the clock carefully. It has 5 divisions between any
two numbers. These show minutes.

Hour Hand takes an hour to move
from one number to another, say
from | to 2 or 4 to 5.

See the clock. Where is the Hour Hand? Where is the
minute hand? What is the time? It is 5 minutes past
12 or simply 12:05.

When the minute hand moves on 2, it becomes 10
minutes past 12 or simply 12:10 ( see figure (i)

Modern Simple Mathematics - 3

: When the minute hand moves on 5, it is 25 minutes past 12 or simply 12:25 ( see figure (ii) i
: When the minute hand reaches 6, it is 30 minutes past 12 or 12:30 ( see figure (iii) :
: When the minute hand reaches 11, it is 55 minutes past 12 or 12:55 ( see figure (iv)

i When the minute hand reaches 12 again i.e. it has made one full round of the

i dial, it is 60 minutes past 12 or 12:60. But now you will observe that Hour

: Hand has reached one (1). It is 1 O’clock. ( see figure (v)

(iii) (iv)
You have seen that when the hour hand moves from 12 to | or 1 number
the minute hand takes one full round in the same time makes an hour.
One full round also means 60 small parts (i.e. 12x5 = 60)

1 Hour = 60 Minutes

To know how many minutes, simply multiply the number by 5 at which
is the minute hand.

Example:

Express in hours and minutes if - Also draw picture to show the time.
Hour hand is between 6 and 7; minute hand is at 3 =

Hour hand is between 10 and 11; minute hand is at 9 =
Hour hand is at 7 and minute hand at 1 =

Hour hand is between 6 and 7 and minute hand at 10 =

Modern Simple Mathematics - 3

EXERCISE-11.2

See the picture of the clock.
1. Where is the Hour Hand = between eee
2. Where is the minute hand = at Be

3. What is the time = past

4. Read out the times from the following clocks.

The minute hand reached
12 and the hour hand moved
from 12 to 1.

The minute hand takes 60 minutes to complete one full round (you can see
60 small divisions on a big clock dial) of the dial and the hour hand takes 60
minutes (or one hour) in moving from one number to another.

— 60 minutes = ot: Hour —

Modern Simple Mathematics - 3

15 minutes past 2 is also called a quarter past two (since 15 minutes
is a quarter of 60).

A)

jor a quarter

half

45 minutes past 2 is also called a quater to 3 as only 15 minutes or a
quater is left to complete 3 hours.

aI-

Or

a quarter
remaining before
3 O’clock

Express the following time as ‘half past’, a quarter past’ or ‘a “quarter to’

Modern Simple Mathematics - 3

Draw picture of the clocks to show the following time:
3:30 6:45 TAS 8:45 9:00

EXERCISE-11.3

1. Write the time under the following clocks:

Small hand between Hour hand between Hour hand between bez
[Jad CJ} (Jee CI [Jad Cl
Big hand at 4 Minute hand at eS Minute hand at ee Es

Time[{__| gl BBS [_|minute past [|| Time [__]minutes past is

Be Where will the Hour Hand and Minute Hand be at

40 minutes past 4
20 minutes past 11

3. If it is a quarter past two now, what will be the time:
(i) after 10 minutes (ii) after 30 minutes

4. Rashid leaves home at half past nine and reaches school at a quarter
to 10. What time does he take to reach the school?

| 5. Azan was called at a quarter to five and after half an hour Jamaat
was started. Tell at what time jamaat was started?

Days and Hours

You know, when there is sunlight it is day and when the sun sets it
is night. One day and one night make one full day.

Example: How many hours are there in 2 days?

Solution: One day = 24 Hours
Two days = 2X 24
48 Hours

How many hours are in :
1. 4 days hours
2. 6 days _ hours

hours

:

. 5 days and 8 hours | ccc hours
Leila
Lassies

3 days and 2 hours

7 days and 5 hours hours

3
4
5
6. 9 days and 4 hours

DAYS, WEEKS, MONTHS AND YEAR

One-week has seven days: Sunday, Monday, Tuesday, Wednesday
Thursday, Friday and Saturday.

One week 7 days

One month 30 days

One year 12 months

Name of Christian (also called Solar) months and number of days in

each of them.

January 31
February 28 or 29
March 31
April

May

June

July

August
September
October
November

December

There is a simple thumb rule to know (and also
remember) the number of days in any month.
Close your fist and count month on the ridge
and furrow of your fingers.

«=== Ridge (Swollen part)

¢=——= Furrow (deep part)

The month that comes on ridge has 31 days.
Rest 30 days. Always start from January. Second
round begins from the month of August.

Modern Simple Mathematics - 3

February and Leap year

February is a special month which has 28 days for 3 years and on every 4th
year it has 29 days. The year in which February has 29 days is always
divisible by 4 and is called LEAP YEAR. In that year there are 366 days in
a year instead of 365 days.

pc ana ee Leap years are 2000, 2004, 1996,
Jan 31 | |\Jan 31 days | 1992, 1988, 1984, 1980, 1976,

Feb 29 ||Feb 28 days | 1972, 1968

Mar 31 | |Mar 31 days all are divisible by 4

Apr 30 | | Apr 30 days 2000 _

May 31 | |May 31 days =A00 =

June 30 | |June 30 days

July 31 | |July 31 days

Aug 31 | |Aug 31 days

Sept 30 | |Sept 30 days

(Note: century year should be
divisible by 400 and not by 4)

Oct 31 | |Oct 31 days
Nov 30 | |Nov 30 days
Dec 31 | |Dec 31 days

Total 366 §f| Total 365 days

EXERCISE-11.5

1. How many days are there in the month of August? Fea days

2. How many days are there in the month of November? Be days

3. Which month of the year is June? ee]

4. Which is the 11th month of the year? ee Aaontis
5. How many months have 31 days? Aone
6. How many months have 30 days?

7. In 1936 February had only? [_] days

Modern Simple Mathematics - 3

Re Te OT ee ea

CHAPTER- 12
Fractional Numbers
See the following figures: —

1 (One) or whole

4 or Half 1 divided into 2 parts

4 or 1 divided into 3 parts

4 or | divided into 4 parts

4 or | divided into 5 parts

i or | divided into 6 parts

4 or | divided into 7 parts

al

1 or 1 divided into 8 parts

3 or | divided into 9 parts

eh |

Zz jor |
o|—

o
=
ol-

ib or | divided into 10 parts

een)

1

3 or One-Half : or One-fifth : or One-eighth
1 :

3 or One-third 1 or One-sixth i or One-ninth
1

40 One-fourth 1 or One-seventh + or One-tenth

Modern Simple Mathematics - 3

Consider the fraction «dn, The number written above the bar (—) is
| called Numerator. It represents the thing or number which is divided.
| And the number written under the bar (—) is called Denominator.
It represents the number of parts into which the number written above
| has been divided.

| taken parts® 1 —Numerator

‘ —— ~~ Symbol of fraction (— bar) also read as upon
| Total parts® 57> — Peamentiigios

41
5 represents one part taken from 5 equal parts of something. It also

| tells the one (whole) has been divided into 5 parts.
Similary

1 represents one part taken from 4 equal parts of something. It also
represents that one (whole) has been divided into 4 parts.

EXERCISE-12.1

| Draw pictures to represent the following as shown below

:

S|- NO ihe Cale
ll

Sa
i

66 Modern Simple Mathematics - 3

EXERCISE-12.2

1. Fill in the blanks. First one is done for you.

Numerator Denominator Fraction Read as

‘One upon

2. Write the Numerators in the following fractional numbers:

o ¢ @ i ® Ga

3. Write the Denominators in the following fractional numbers:

© 1 @ * @ § 87

4. Write as fractional numbers

(i) Two-thirds (ii) Three-fourths (ili) One-third
(iv) Four-eights (v) Three-sevenths (vi) 5 upon 8
(vii) Seven upon ten (viii) One-half (ix) Three-twelfth

5. Hamid had 10 rupees. He spent 3 rupees. Express it in fractional
number.
6. What fraction is 17 marks out of 25.

Modern Simple Mathematics - 3

Like fractions:
Fractional numbers with equal denominators are called like fractions.

BI

Look at the above pictures. : 2 3 These are fractions whose denomi-
nators are equal (4)

Addition of Like fractions:

Example () 777 | | | | |+ _l[ GG 1 |
2

~

eS)
7 7
= WMLLA_\_|
2.
5
3) 1 = 4
6 = 6 6
Example (3)
3 Ae
Add 10 and 10
opt eet
102-10 10 10

While adding like fractions, we add numerators of the fractions and
write denominator as it is.

Modern Simple Mathematics -

EXERCISE-12.3

1. Sort out fractions with equal denominators and add them.

ee ce Bei 7
(i) 54S 5 6°? SS} 24 (ii) Jap Oe Py,
ay Bee Oe ae
(ill) 9, 75 5. 9

2. Fill in the blanks.

(i) 1,3-u3_8

gq 2 -
(ii) 4+2 = a =
@ 24+¢-80-4

es

odern Simple Mathematics -

Subtraction of like fractions:-

Example-1: 1
aS There are three 3 parts to make one whole. We

One part
coloured \P eg
Two parts left «<_S

uncoloured
Example-2: ("TT -T-1 1]
Each part of the strip is é- 6 parts together make 8 or whole.

ETT} How many parts are there?

write it as 4
gy If we colour one 4) part, how much will be left?

Shaded = parts or é shaded. Of these 4 shaded parts 3 have been
cut. How many shaded parts are left now?

3 parts cut 1 part left

Parts left.
4 3-4-3 1
me Gh ge oe
one part (or 5 left.

Example-3:

Modern Simple Mathematics -

Example:4

While subtracting like fractions we subtract Numerator of second frac-

tion from the numerator of first fraction and write denominator as it is.

EXERCISE-12.4

1. Fill in the blanks:

2 1 1. a
oe 3 5 5
ae | 3. +E.
gg 9 9

(iii)

(iv)

2. Find the diference of the following like fractions:

OQ 7 17 Gi) 4 ~ at Gos.
“Des sso Dies ae
25 (vi) 49 ~ 19

Modern Simple Mathematics - 3

= CHAPTER - 13 Geometrical Shapes

Look at the following figures and learn them.

oN’ ee [= —

Point Line spent

A closed curve which does not cross itself is called a simple closed
curve. Here are some closed curves.

ae

| EXERCISE.13 |

1. Name the Shapes: o\ (i) AA Sti Soe (iv) om
“MC w<— wii (viii) [| (ix)

2. How many traingles are there in the following figures:

@) A» ok

Line

Modern Simple Mathematics - 3